Phil Wolf, owner of Wolf Automotive, said the billboard asks a legitimate question about Obama's alleged lack of documentation of his American birth.
"President or Jihad?" the billboard reads. "Wake up, America! Remember Fort Hood!"
Wolf said politicians have not been held accountable.
"This man is not telling the truth," Wolf said. "He should prove he's an American."
Bobby Clark of the liberal online network Progress Now Colorado is organizing a boycott of Wolf Automotive. Clark said "birthers" and "teabaggers" like Wolf have been emboldened by mainstream Republican politicians and pundits.
"When people like Rush Limbaugh, Peter Boyles, Glenn Beck and elected officials like Sarah Palin and Sen. Dave Schultheis openly question the president's citizenship and compare him to terrorists, it gives permission to this kind of speech," Clark said. "It's hateful. It's racist. It's outrageous."
Wolf denied he's racist. He said he's written in Alan Keyes, a conservative political activist and African- American, as his presidential choice.
Wolf's cartoonish billboard also drew criticism from the Anti-Defamation League.
"This billboard exploits the recent tragic shooting at Fort Hood in a context replete with bigotry," said ADL Mountain States director Bruce DeBoskey. "It is divisive and offensive, and perpetuates harmful stereotypes about Muslims."
Wolf said that fear of asking the hard questions led to the carnage at Fort Hood by American-born Muslim Nidal Malik Hasan.
"It's a disgrace that political correctness is ruining this country," Wolf said. "We were 'too sensitive' to question Hasan . . . because he's Muslim.
The billboard cost Wolf "a couple thousand dollars," he said, and it might lose him some customers.
"If it does, it doesn't matter," Wolf said. "I've had two ladies go home terrified because of the threats we've had."
Wolf, who owns dealerships in Colorado, Wyoming and Montana, said the Obama administration has ruined the auto industry by interfering in it.
This billboard isn't likely to help sell cars, said Ibrahim Hooper, spokesman for the D.C.-based Council on American-Islamic Relations.
"It's an offensive billboard on several levels," Hooper said. "It's disrespectful of the presidency and Islam. It's a racist depiction as well."